Question: $(7-10i)-(3+30i)=$ Express your answer in the form $(a+bi)$.
Answer: Background Complex numbers can be added or subtracted by separately adding or subtracting their real and imaginary terms. To add or subtract complex numbers: Expand parentheses (attending to minus signs outside of parentheses if necessary) Combine all real terms (terms that do not contain $i$ ), and add or subtract them. Combine all imaginary terms (terms that contain $i$ ), and add or subtract them. Combining Like Terms $\begin{aligned} ({7}{-10}i)-({3}+{30}i)&={7}{-10}i-{3}-{30}i \\\\ &={7}-{3}-{10}i-{30}i \\\\ &={4}{-40}i \end{aligned}$ Summary $({7}{-10}i)-({3}+{30}i)={4}{-40}i$